A Catalan Transform and Related Transformations on Integer Sequences

Paul Barry
School of Science
Waterford Institute of Technology
Ireland

Abstract:
We introduce and study an invertible transformation on integer
sequences related to the Catalan numbers. Transformation pairs are
identified among classical sequences. A closely related
transformation which we call the generalized Ballot transform is also studied,
along with associated transformations. Results
concerning the Fibonacci, Jacobsthal and Pell numbers are derived. Finally, we
derive results about combined transformations.